Detecting nonlinear patterns in physiological signals

The authors discuss a novel method to detect possible nonlinear structure in signals obtained from dynamical systems, which includes those obtained from physiological systems. The sampled discrete time series is first mapped onto a phase space by the method of delays. The vector series in phase space is partitioned into a finite number of clusters by the k-means technique. The determinant of the within-class scatter matrix provides an estimate of the hyper-ellipsoidal volume of the partitioned phase space. The objective is to look for significant differences in the hyper-ellipsoidal scatter volume between the original data and its corresponding surrogate realizations. The surrogate data sets were generated by the Iterated Amplitude Adjusted Fourier Transform technique (IAAFT). The null hypothesis addressed here is that the original data is a static nonlinear transform of a linearly correlated noise. The data sets analyzed include the uterine electromyography obtained during active labor.